Unlike the other examples, this case is not well-specified, as \(k(\cdot |\theta )\ne f(\cdot )\)  for every \(\theta \) . This makes the definition of true or data-generating number of clusters more delicate. Nonetheless, being an example with constant data, one would hope the posterior of the number of clusters to concentrate on one cluster.
However, even in such a limiting case, [1]} show that under (REF ) with fixed concentration parameter \(\text{pr}(K_n=1|X_{1:n})\)  does not converge to 1 as \(n\)  diverges.
